Canonical metrics and Härder-Narasimhan filtration

Julien Keller (1)

1 I2M - Institut de Mathématiques de Marseille

The algebraic notion of Gieseker stability is related to the existence of balanced metrics which are zeros of a certain moment map. We investigate some properties of balanced metrics relative to the Harder-Narasimhan filtration of a vector bundle and to blowups in the case of projective surfaces.

Mots clés: surface; Mumford stable; Hermitian-Einstein metric; balanced metric; Harder-Narasimhan; vector bundle; manifold; blow up

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Julien Keller. Canonical metrics and Härder-Narasimhan filtration: Proceedings of the 8th International Workshop on Complex Structures and Vector Fields Institute of Mathematics and Informatics, Bulgaria, 21 – 26 August 2006. 8th International Workshop on Complex Structures and Vector Fields, Stancho Dimiev (Bulgarian Academy of Sciences, Bulgaria), Kouei Sekigawa (Niigata University, Japan), Aug 2006, Plovdiv, Bulgaria. ⟨10.1142/6501⟩. ⟨hal-01282570⟩